(Difficulty: E = Easy, M = Medium, and T = Tough)
Multiple Choice: Conceptual
Easy:
PV and discount rate Answer: a Diff: E
1. You have determined the profitability of a planned project by finding
the present value of all the cash flows from that project. Which of the following would cause the project to look more appealing in terms of the present value of those cash flows?
a. The discount rate decreases.
b. The cash flows are extended over a longer period of time, but the total amount of the cash flows remains the same.
c. The discount rate increases. d. Statements b and c are correct. e. Statements a and b are correct.
Time value concepts Answer: e Diff: E
2. Which of the following statements is most correct?
a. A 5-year $100 annuity due will have a higher present value than a 5-year $100 ordinary annuity.
b. A 15-year mortgage will have larger monthly payments than a 30-year mortgage of the same amount and same interest rate.
c. If an investment pays 10 percent interest compounded annually, its effective rate will also be 10 percent.
d. Statements a and c are correct.
e. All of the statements above are correct.
Time value concepts Answer: d Diff: E
3. The future value of a lump sum at the end of five years is $1,000. The
nominal interest rate is 10 percent and interest is compounded semiannually. Which of the following statements is most correct?
a. The present value of the $1,000 is greater if interest is compounded monthly rather than semiannually.
b. The effective annual rate is greater than 10 percent. c. The periodic interest rate is 5 percent.
d. Statements b and c are correct.
e. All of the statements above are correct.
CHAPTER 6
Time value concepts Answer: d Diff: E
4. Which of the following statements is most correct?
a. The present value of an annuity due will exceed the present value of an ordinary annuity (assuming all else equal).
b. The future value of an annuity due will exceed the future value of an ordinary annuity (assuming all else equal).
c. The nominal interest rate will always be greater than or equal to the effective annual interest rate.
d. Statements a and b are correct.
e. All of the statements above are correct.
Time value concepts Answer: e Diff: E
5. Which of the following investments will have the highest future value
at the end of 5 years? Assume that the effective annual rate for all investments is the same.
a. A pays $50 at the end of every 6-month period for the next 5 years (a total of 10 payments).
b. B pays $50 at the beginning of every 6-month period for the next 5 years (a total of 10 payments).
c. C pays $500 at the end of 5 years (a total of one payment).
d. D pays $100 at the end of every year for the next 5 years (a total of 5 payments).
e. E pays $100 at the beginning of every year for the next 5 years (a total of 5 payments).
Effective annual rate Answer: b Diff: E
6. Which of the following bank accounts has the highest effective annual
return?
a. An account that pays 10 percent nominal interest with monthly com-pounding.
b. An account that pays 10 percent nominal interest with daily com-pounding.
c. An account that pays 10 percent nominal interest with annual com-pounding.
d. An account that pays 9 percent nominal interest with daily com-pounding.
e. All of the investments above have the same effective annual return.
Effective annual rate Answer: d Diff: E
7. You are interested in investing your money in a bank account. Which of
the following banks provides you with the highest effective rate of interest?
a. Bank 1; 8 percent with monthly compounding. b. Bank 2; 8 percent with annual compounding. c. Bank 3; 8 percent with quarterly compounding.
Amortization Answer: b Diff: E
8. Your family recently obtained a 30-year (360-month) $100,000 fixed-rate
mortgage. Which of the following statements is most correct? (Ignore all taxes and transactions costs.)
a. The remaining balance after three years will be $100,000 less the total amount of interest paid during the first 36 months.
b. The proportion of the monthly payment that goes towards repayment of principal will be higher 10 years from now than it will be this year. c. The monthly payment on the mortgage will steadily decline over time. d. All of the statements above are correct.
e. None of the statements above is correct.
Amortization Answer: e Diff: E
9. Frank Lewis has a 30-year, $100,000 mortgage with a nominal interest
rate of 10 percent and monthly compounding. Which of the following statements regarding his mortgage is most correct?
a. The monthly payments will decline over time.
b. The proportion of the monthly payment that represents interest will be lower for the last payment than for the first payment on the loan. c. The total dollar amount of principal being paid off each month gets
larger as the loan approaches maturity. d. Statements a and c are correct.
e. Statements b and c are correct.
Quarterly compounding Answer: e Diff: E
10. Your bank account pays an 8 percent nominal rate of interest. The
interest is compounded quarterly. Which of the following statements is most correct?
a. The periodic rate of interest is 2 percent and the effective rate of interest is 4 percent.
b. The periodic rate of interest is 8 percent and the effective rate of interest is greater than 8 percent.
c. The periodic rate of interest is 4 percent and the effective rate of interest is 8 percent.
d. The periodic rate of interest is 8 percent and the effective rate of interest is 8 percent.
e. The periodic rate of interest is 2 percent and the effective rate of interest is greater than 8 percent.
Medium:
Annuities Answer: c Diff: M
11. Suppose someone offered you the choice of two equally risky annuities,
each paying $10,000 per year for five years. One is an ordinary (or deferred) annuity, the other is an annuity due. Which of the following statements is most correct?
a. The present value of the ordinary annuity must exceed the present value of the annuity due, but the future value of an ordinary annuity may be less than the future value of the annuity due.
b. The present value of the annuity due exceeds the present value of the ordinary annuity, while the future value of the annuity due is less than the future value of the ordinary annuity.
c. The present value of the annuity due exceeds the present value of the ordinary annuity, and the future value of the annuity due also exceeds the future value of the ordinary annuity.
d. If interest rates increase, the difference between the present value of the ordinary annuity and the present value of the annuity due remains the same.
e. Statements a and d are correct.
Time value concepts Answer: e Diff: M
12. A $10,000 loan is to be amortized over 5 years, with annual end-of-year
payments. Given the following facts, which of these statements is most correct?
a. The annual payments would be larger if the interest rate were lower. b. If the loan were amortized over 10 years rather than 5 years, and if
the interest rate were the same in either case, the first payment would include more dollars of interest under the 5-year amortization plan.
c. The last payment would have a higher proportion of interest than the first payment.
d. The proportion of interest versus principal repayment would be the same for each of the 5 payments.
e. The proportion of each payment that represents interest as opposed to repayment of principal would be higher if the interest rate were higher.
Time value concepts Answer: e Diff: M
13. Which of the following is most correct?
a. The present value of a 5-year annuity due will exceed the present value of a 5-year ordinary annuity. (Assume that both annuities pay $100 per period and there is no chance of default.)
b. If a loan has a nominal rate of 10 percent, then the effective rate can never be less than 10 percent.
c. If there is annual compounding, then the effective, periodic, and nominal rates of interest are all the same.
d. Statements a and c are correct.
e. All of the statements above are correct.
Time value concepts Answer: c Diff: M
14. Which of the following statements is most correct?
a. An investment that compounds interest semiannually, and has a nominal rate of 10 percent, will have an effective rate less than 10 percent.
b. The present value of a 3-year $100 annuity due is less than the present value of a 3-year $100 ordinary annuity.
c. The proportion of the payment of a fully amortized loan that goes toward interest declines over time.
d. Statements a and c are correct.
e. None of the statements above is correct.
Tough:
Time value concepts Answer: e Diff: T
15. Which of the following statements is most correct?
a. The first payment under a 3-year, annual payment, amortized loan for $1,000 will include a smaller percentage (or fraction) of interest if the interest rate is 5 percent than if it is 10 percent.
b. If you are lending money, then, based on effective interest rates, you should prefer to lend at a 10 percent nominal, or quoted, rate but with semiannual payments, rather than at a 10.1 percent nominal rate with annual payments. However, as a borrower you should prefer the annual payment loan.
c. The value of a perpetuity (say for $100 per year) will approach infinity as the interest rate used to evaluate the perpetuity approaches zero.
d. Statements b and c are correct.
Multiple Choice: Problems
Easy:
FV of a sum Answer: b Diff: E
16. You deposited $1,000 in a savings account that pays 8 percent interest,
compounded quarterly, planning to use it to finish your last year in college. Eighteen months later, you decide to go to the Rocky Mountains to become a ski instructor rather than continue in school, so you close out your account. How much money will you receive?
a. $1,171 b. $1,126 c. $1,082 d. $1,163 e. $1,008
FV of an annuity Answer: e Diff: E
17. What is the future value of a 5-year ordinary annuity with annual
payments of $200, evaluated at a 15 percent interest rate? a. $ 670.44
b. $ 842.91 c. $1,169.56 d. $1,522.64 e. $1,348.48
FV of an annuity Answer: a Diff: E N
18. Today is your 23rd birthday. Your aunt just gave you $1,000. You have
used the money to open up a brokerage account. Your plan is to contribute an additional $2,000 to the account each year on your birthday, up through and including your 65th birthday, starting next
year. The account has an annual expected return of 12 percent. How much do you expect to have in the account right after you make the
final $2,000 contribution on your 65th birthday?
a. $2,045,442 b. $1,811,996 c. $2,292,895 d. $1,824,502 e. $2,031,435
FV of annuity due Answer: d Diff: E N 19. Today is Janet’s 23rd birthday. Starting today, Janet plans to begin
saving for her retirement. Her plan is to contribute $1,000 to a brokerage account each year on her birthday. Her first contribution will
take place today. Her 42nd and final contribution will take place on her
64th birthday. Her aunt has decided to help Janet with her savings, which
is why she gave Janet $10,000 today as a birthday present to help get her account started. Assume that the account has an expected annual return of 10 percent. How much will Janet expect to have in her account on her 65th birthday? a. $ 985,703.62 b. $1,034,488.80 c. $1,085,273.98 d. $1,139,037.68 e. $1,254,041.45
PV of an annuity Answer: a Diff: E
20. What is the present value of a 5-year ordinary annuity with annual
payments of $200, evaluated at a 15 percent interest rate? a. $ 670.43
b. $ 842.91 c. $1,169.56 d. $1,348.48 e. $1,522.64
PV of a perpetuity Answer: c Diff: E
21. You have the opportunity to buy a perpetuity that pays $1,000 annually.
Your required rate of return on this investment is 15 percent. You should be essentially indifferent to buying or not buying the investment if it were offered at a price of
a. $5,000.00 b. $6,000.00 c. $6,666.67 d. $7,500.00 e. $8,728.50
PV of an uneven CF stream Answer: b Diff: E
22. A real estate investment has the following expected cash flows:
Year Cash Flows
1 $10,000
2 25,000
3 50,000
4 35,000
The discount rate is 8 percent. What is the investment’s present value? a. $103,799
b. $ 96,110 c. $ 95,353 d. $120,000 e. $ 77,592
PV of an uneven CF stream Answer: c Diff: E
23. Assume that you will receive $2,000 a year in Years 1 through 5, $3,000
a year in Years 6 through 8, and $4,000 in Year 9, with all cash flows to be received at the end of the year. If you require a 14 percent rate of return, what is the present value of these cash flows?
a. $ 9,851 b. $13,250 c. $11,714 d. $15,129 e. $17,353
Required annuity payments Answer: b Diff: E
24. If a 5-year ordinary annuity has a present value of $1,000, and if the
interest rate is 10 percent, what is the amount of each annuity payment? a. $240.42
b. $263.80 c. $300.20 d. $315.38 e. $346.87
Quarterly compounding Answer: a Diff: E
25. If $100 is placed in an account that earns a nominal 4 percent,
compounded quarterly, what will it be worth in 5 years? a. $122.02
b. $105.10 c. $135.41 d. $120.90 e. $117.48
Growth rate Answer: d Diff: E
26. In 1958 the average tuition for one year at an Ivy League school was
$1,800. Thirty years later, in 1988, the average cost was $13,700. What was the growth rate in tuition over the 30-year period?
a. 12% b. 9% c. 6% d. 7% e. 8%
Effect of inflation Answer: c Diff: E
27. At an inflation rate of 9 percent, the purchasing power of $1 would be
cut in half in 8.04 years. How long to the nearest year would it take the purchasing power of $1 to be cut in half if the inflation rate were only 4 percent? a. 12 years b. 15 years c. 18 years d. 20 years e. 23 years
Interest rate Answer: b Diff: E
28. South Penn Trucking is financing a new truck with a loan of $10,000 to
be repaid in 5 annual end-of-year installments of $2,504.56. What annual interest rate is the company paying?
a. 7% b. 8% c. 9% d. 10% e. 11%
Effective annual rate Answer: c Diff: E
29. Gomez Electronics needs to arrange financing for its expansion program.
Bank A offers to lend Gomez the required funds on a loan in which interest must be paid monthly, and the quoted rate is 8 percent. Bank B will charge 9 percent, with interest due at the end of the year. What is the difference in the effective annual rates charged by the two banks? a. 0.25% b. 0.50% c. 0.70% d. 1.00% e. 1.25%
Effective annual rate Answer: b Diff: E
30. You recently received a letter from Cut-to-the-Chase National Bank that
offers you a new credit card that has no annual fee. It states that the annual percentage rate (APR) is 18 percent on outstanding balances. What is the effective annual interest rate? (Hint: Remember these companies bill you monthly.)
a. 18.81% b. 19.56% c. 19.25% d. 20.00% e. 18.00%
Effective annual rate Answer: b Diff: E
31. Which of the following investments has the highest effective annual
rate (EAR)? (Assume that all CDs are of equal risk.) a. A bank CD that pays 10 percent interest quarterly. b. A bank CD that pays 10 percent monthly.
c. A bank CD that pays 10.2 percent annually. d. A bank CD that pays 10 percent semiannually.
e. A bank CD that pays 9.6 percent daily (on a 365-day basis).
Effective annual rate Answer: c Diff: E
32. You want to borrow $1,000 from a friend for one year, and you propose
to pay her $1,120 at the end of the year. She agrees to lend you the $1,000, but she wants you to pay her $10 of interest at the end of each
of the first 11 months plus $1,010 at the end of the 12th month. How
much higher is the effective annual rate under your friend’s proposal than under your proposal?
a. 0.00% b. 0.45% c. 0.68% d. 0.89% e. 1.00%
Effective annual rate Answer: b Diff: E
33. Elizabeth has $35,000 in an investment account. Her goal is to have the
account grow to $100,000 in 10 years without having to make any additional contributions to the account. What effective annual rate of interest would she need to earn on the account in order to meet her goal?
a. 9.03% b. 11.07% c. 10.23% d. 8.65% e. 12.32%
Effective annual rate Answer: a Diff: E
34. Which one of the following investments provides the highest effective
rate of return?
a. An investment that has a 9.9 percent nominal rate and quarterly annual compounding.
b. An investment that has a 9.7 percent nominal rate and daily (365) compounding.
c. An investment that has a 10.2 percent nominal rate and annual compounding.
d. An investment that has a 10 percent nominal rate and semiannual compounding.
e. An investment that has a 9.6 percent nominal rate and monthly compounding.
Effective annual rate Answer: b Diff: E
35. Which of the following investments would provide an investor the
highest effective annual rate of return?
a. An investment that has a 9 percent nominal rate with semiannual compounding.
b. An investment that has a 9 percent nominal rate with quarterly compounding.
c. An investment that has a 9.2 percent nominal rate with annual compounding.
d. An investment that has an 8.9 percent nominal rate with monthly compounding.
e. An investment that has an 8.9 percent nominal rate with quarterly compounding.
Nominal and effective rates Answer: b Diff: E
36. An investment pays you 9 percent interest compounded semiannually. A
second investment of equal risk, pays interest compounded quarterly. What nominal rate of interest would you have to receive on the second investment in order to make you indifferent between the two investments? a. 8.71%
b. 8.90% c. 9.00% d. 9.20% e. 9.31%
Time for a sum to double Answer: d Diff: E
37. You are currently investing your money in a bank account that has a
nominal annual rate of 7 percent, compounded monthly. How many years will it take for you to double your money?
a. 8.67 b. 9.15 c. 9.50 d. 9.93
e. 10.25
Time for lump sum to grow Answer: e Diff: E N
38. Jill currently has $300,000 in a brokerage account. The account pays a
10 percent annual interest rate. Assuming that Jill makes no additional contributions to the account, how many years will it take for her to have $1,000,000 in the account?
a. 23.33 years b. 3.03 years c. 16.66 years d. 33.33 years e. 12.63 years
Time value of money and retirement Answer: b Diff: E 39. Today, Bruce and Brenda each have $150,000 in an investment account.
No other contributions will be made to their investment accounts. Both have the same goal: They each want their account to reach $1 million, at which time each will retire. Bruce has his money invested in risk-free securities with an expected annual return of 5 percent. Brenda has her money invested in a stock fund with an expected annual return of
10 percent. How many years after Brenda retires will Bruce retire? a. 12.6
b. 19.0 c. 19.9 d. 29.4 e. 38.9
Monthly loan payments Answer: c Diff: E
40. You are considering buying a new car. The sticker price is $15,000 and
you have $2,000 to put toward a down payment. If you can negotiate a nominal annual interest rate of 10 percent and you wish to pay for the car over a 5-year period, what are your monthly car payments?
a. $216.67 b. $252.34
c. $276.21
d. $285.78 e. $318.71
Remaining loan balance Answer: a Diff: E
41. A bank recently loaned you $15,000 to buy a car. The loan is for five
years (60 months) and is fully amortized. The nominal rate on the loan is 12 percent, and payments are made at the end of each month. What will be
the remaining balance on the loan after you make the 30th payment?
a. $ 8,611.17 b. $ 8,363.62
d. $ 8,637.38 e. $ 7,599.03
Remaining loan balance Answer: b Diff: E
42. Robert recently borrowed $20,000 to purchase a new car. The car loan
is fully amortized over 4 years. In other words, the loan has a fixed monthly payment, and the loan balance will be zero after the final monthly payment is made. The loan has a nominal interest rate of 12 percent with monthly compounding. Looking ahead, Robert thinks there is a chance that he will want to pay off the loan early, after 3 years (36 months). What will be the remaining balance on the loan
after he makes the 36th payment?
a. $7,915.56 b. $5,927.59 c. $4,746.44 d. $4,003.85 e. $5,541.01
Remaining mortgage balance Answer: c Diff: E
43. Jerry and Faith Hudson recently obtained a 30-year (360-month),
$250,000 mortgage with a 9 percent nominal interest rate. What will be the remaining balance on the mortgage after five years (60 months)?
a. $239,024 b. $249,307 c. $239,700 d. $237,056 e. $212,386
Remaining mortgage balance Answer: d Diff: E
44. You just bought a house and have a $150,000 mortgage. The mortgage is
for 30 years and has a nominal rate of 8 percent (compounded monthly). After 36 payments (3 years) what will be the remaining balance on your mortgage? a. $110,376.71 b. $124,565.82 c. $144,953.86 d. $145,920.12 e. $148,746.95
Remaining mortgage balance Answer: d Diff: E
45. Your family purchased a house three years ago. When you bought the
house you financed it with a $160,000 mortgage with an 8.5 percent nominal interest rate (compounded monthly). The mortgage was for 15 years (180 months). What is the remaining balance on your mortgage today?
b. $103,300 c. $125,745 d. $141,937 e. $159,998
Remaining mortgage balance Answer: c Diff: E
46. You recently took out a 30-year (360 months), $145,000 mortgage. The
mortgage payments are made at the end of each month and the nominal interest rate on the mortgage is 7 percent. After five years (60 payments), what will be the remaining balance on the mortgage?
a. $ 87,119 b. $136,172 c. $136,491 d. $136,820 e. $143,527
Remaining mortgage balance Answer: b Diff: E
47. A 30-year, $175,000 mortgage has a nominal interest rate of 7.45
percent. Assume that all payments are made at the end of each month. What will be the remaining balance on the mortgage after 5 years (60 monthly payments)? a. $ 63,557 b. $165,498 c. $210,705 d. $106,331 e. $101,942
Amortization Answer: c Diff: E
48. The Howe family recently bought a house. The house has a 30-year,
$165,000 mortgage with monthly payments and a nominal interest rate of 8 percent. What is the total dollar amount of interest the family will pay during the first three years of their mortgage? (Assume that all payments are made at the end of the month.)
a. $ 3,297.78 b. $38,589.11 c. $39,097.86 d. $43,758.03 e. $44,589.11
FV under monthly compounding Answer: a Diff: E N
49. Bill plans to deposit $200 into a bank account at the end of every
month. The bank account has a nominal interest rate of 8 percent and interest is compounded monthly. How much will Bill have in the account at the end of 2½ years (30 months)?
a. $ 6,617.77 b. $ 502.50 c. $ 6,594.88
Medium:
Monthly vs. quarterly compounding Answer: c Diff: M 50. On its savings accounts, the First National Bank offers a 5 percent
nominal interest rate that is compounded monthly. Savings accounts at the Second National Bank have the same effective annual return, but interest is compounded quarterly. What nominal rate does the Second National Bank offer on its savings accounts?
a. 5.12% b. 5.00% c. 5.02% d. 1.28% e. 5.22%
Present value Answer: c Diff: M N
51. Which of the following securities has the largest present value?
Assume in all cases that the annual interest rate is 8 percent and that there are no taxes.
a. A five-year ordinary annuity that pays you $1,000 each year. b. A five-year zero coupon bond that has a face value of $7,000.
c. A preferred stock issue that pays an $800 annual dividend in perpetuity. (Assume that the first dividend is received one year from today.)
d. A seven-year zero coupon bond that has a face value of $8,500.
e. A security that pays you $1,000 at the end of 1 year, $2,000 at the end of 2 years, and $3,000 at the end of 3 years.
PV under monthly compounding Answer: b Diff: M
52. You have just bought a security that pays $500 every six months. The
security lasts for 10 years. Another security of equal risk also has a maturity of 10 years, and pays 10 percent compounded monthly (that is, the nominal rate is 10 percent). What should be the price of the security that you just purchased?
a. $6,108.46 b. $6,175.82 c. $6,231.11 d. $6,566.21 e. $7,314.86
PV under non-annual compounding Answer: c Diff: M
53. You have been offered an investment that pays $500 at the end of every
6 months for the next 3 years. The nominal interest rate is 12 percent; however, interest is compounded quarterly. What is the present value of the investment?
a. $2,458.66 b. $2,444.67 c. $2,451.73
PV of an annuity Answer: a Diff: M
54. Your subscription to Jogger’s World Monthly is about to run out and you
have the choice of renewing it by sending in the $10 a year regular rate or of getting a lifetime subscription to the magazine by paying $100. Your cost of capital is 7 percent. How many years would you have to live to make the lifetime subscription the better buy? Payments for the regular subscription are made at the beginning of each year. (Round up if necessary to obtain a whole number of years.)
a. 15 years
b. 10 years c. 18 years d. 7 years e. 8 years
FV of an annuity Answer: e Diff: M
55. Your bank account pays a nominal interest rate of 6 percent, but
interest is compounded daily (on a 365-day basis). Your plan is to deposit $500 in the account today. You also plan to deposit $1,000 in the account at the end of each of the next three years. How much will you have in the account at the end of three years, after making your final deposit? a. $2,591 b. $3,164 c. $3,500 d. $3,779 e. $3,788
FV of an annuity Answer: c Diff: M
56. Terry Austin is 30 years old and is saving for her retirement. She is
planning on making 36 contributions to her retirement account at the beginning of each of the next 36 years. The first contribution will be made today (t = 0) and the final contribution will be made 35 years from today (t = 35). The retirement account will earn a return of 10 percent a year. If each contribution she makes is $3,000, how much will be in the retirement account 35 years from now (t = 35)?
a. $894,380 b. $813,073 c. $897,380 d. $987,118 e. $978,688
FV of an annuity Answer: d Diff: M N
57. Today is your 20th birthday. Your parents just gave you $5,000 that you
plan to use to open a stock brokerage account. Your plan is to add $500 to the account each year on your birthday. Your first $500
contribution will come one year from now on your 21st birthday. Your 45th
and final $500 contribution will occur on your 65th birthday. You plan
to withdraw $5,000 from the account five years from now on your 25th
birthday to take a trip to Europe. You also anticipate that you will
need to withdraw $10,000 from the account 10 years from now on your 30th
birthday to take a trip to Asia. You expect that the account will have an average annual return of 12 percent. How much money do you anticipate that you will have in the account on your 65th birthday,
following your final contribution? a. $385,863
b. $413,028 c. $457,911 d. $505,803 e. $566,498
FV of annuity due Answer: d Diff: M
58. You are contributing money to an investment account so that you can
purchase a house in five years. You plan to contribute six payments of $3,000 a year. The first payment will be made today (t = 0) and the final payment will be made five years from now (t = 5). If you earn 11 percent in your investment account, how much money will you have in the account five years from now (at t = 5)?
a. $19,412 b. $20,856 c. $21,683
d. $23,739
e. $26,350
FV of annuity due Answer: e Diff: M
59. Today is your 21st birthday, and you are opening up an investment
account. Your plan is to contribute $2,000 per year on your birthday
and the first contribution will be made today. Your 45th, and final,
contribution will be made on your 65th birthday. If you earn 10 percent
a year on your investments, how much money will you have in the account
on your 65th birthday, immediately after making your final contribution?
a. $1,581,590.64 b. $1,739,749.71 c. $1,579,590.64 d. $1,387,809.67 e. $1,437,809.67
FV of a sum Answer: d Diff: M
60. Suppose you put $100 into a savings account today, the account pays a
nominal annual interest rate of 6 percent, but compounded semiannually, and you withdraw $100 after 6 months. What would your ending balance be 20 years after the initial $100 deposit was made?
a. $226.20 b. $115.35 c. $ 62.91 d. $ 9.50 e. $ 3.00
FV under monthly compounding Answer: e Diff: M
61. You just put $1,000 in a bank account that pays 6 percent nominal annual
interest, compounded monthly. How much will you have in your account after 3 years? a. $1,006.00 b. $1,056.45 c. $1,180.32 d. $1,191.00 e. $1,196.68
FV under monthly compounding Answer: d Diff: M
62. Steven just deposited $10,000 in a bank account that has a 12 percent
nominal interest rate, and the interest is compounded monthly. Steven also plans to contribute another $10,000 to the account one year (12 months) from now and another $20,000 to the account two years from now. How much will be in the account three years (36 months) from now?
a. $57,231 b. $48,993 c. $50,971 d. $49,542 e. $49,130
FV under daily compounding Answer: a Diff: M
63. You have $2,000 invested in a bank account that pays a 4 percent
nominal annual interest with daily compounding. How much money will you have in the account at the end of July (in 132 days)? (Assume there are 365 days in each year.)
a. $2,029.14 b. $2,028.93 c. $2,040.00 d. $2,023.44 e. $2,023.99
FV under daily compounding Answer: d Diff: M N
64. The Martin family recently deposited $1,000 in a bank account that pays
a 6 percent nominal interest rate. Interest in the account will be compounded daily (365 days = 1 year). How much will they have in the account after 5 years?
a. $1,000.82 b. $1,433.29 c. $1,338.23 d. $1,349.82 e. $1,524.77
FV under non-annual compounding Answer: d Diff: M
65. Josh and John (2 brothers) are each trying to save enough money to buy
their own cars. Josh is planning to save $100 from every paycheck. (He is paid every 2 weeks.) John plans to put aside $150 each month but has already saved $1,500. Interest rates are currently quoted at 10 percent. Josh’s bank compounds interest every two weeks while John’s bank compounds interest monthly. At the end of 2 years they will each spend all their savings on a car. (Each brother will buy a car.) What is the price of the most expensive car purchased?
a. $5,744.29 b. $5,807.48 c. $5,703.02 d. $5,797.63 e. $5,898.50
FV under quarterly compounding Answer: c Diff: M
66. An investment pays $100 every six months (semiannually) over the next
2.5 years. Interest, however, is compounded quarterly, at a nominal rate of 8 percent. What is the future value of the investment after 2.5 years? a. $520.61 b. $541.63 c. $542.07 d. $543.98 e. $547.49
FV under quarterly compounding Answer: d Diff: M
67. Rachel wants to take a trip to England in 3 years, and she has started
a savings account today to pay for the trip. Today (8/1/02) she made an initial deposit of $1,000. Her plan is to add $2,000 to the account one year from now (8/1/03) and another $3,000 to the account two years from now (8/1/04). The account has a nominal interest rate of 7 percent, but the interest is compounded quarterly. How much will Rachel have in the account three years from today (8/1/05)?
a. $6,724.84 b. $6,701.54 c. $6,895.32 d. $6,744.78 e. $6,791.02
Non-annual compounding Answer: c Diff: M N
68. Katherine wants to open a savings account, and she has obtained account
information from two banks. Bank A has a nominal annual rate of 9 percent, with interest compounded quarterly. Bank B offers the same effective annual rate, but it compounds interest monthly. What is the nominal annual rate of return for a savings account from Bank B?
a. 8.906% b. 8.920% c. 8.933% d. 8.951% e. 9.068%
FV of an uneven CF stream Answer: e Diff: M
69. You are interested in saving money for your first house. Your plan is
to make regular deposits into a brokerage account that will earn 14 percent. Your first deposit of $5,000 will be made today. You also plan to make four additional deposits at the beginning of each of the next four years. Your plan is to increase your deposits by 10 percent a year. (That is, you plan to deposit $5,500 at t = 1, and $6,050 at t = 2, etc.) How much money will be in your account after five years? a. $24,697.40
b. $30,525.00 c. $32,485.98 d. $39,362.57 e. $44,873.90
FV of an uneven CF stream Answer: d Diff: M
70. You just graduated, and you plan to work for 10 years and then to leave
for the Australian “Outback” bush country. You figure you can save $1,000 a year for the first 5 years and $2,000 a year for the next 5 years. These savings cash flows will start one year from now. In addition, your family has just given you a $5,000 graduation gift. If you put the gift now, and your future savings when they start, into an account that pays 8 percent compounded annually, what will your financial “stake” be when you leave for Australia 10 years from now? a. $21,432
b. $28,393 c. $16,651 d. $31,148 e. $20,000
FV of an uneven CF stream Answer: c Diff: M N
71. Erika opened a savings account today and she immediately put $10,000
into it. She plans to contribute another $20,000 one year from now, and $50,000 two years from now. The savings account pays a 6 percent annual interest rate. If she makes no other deposits or withdrawals, how much will she have in the account 10 years from today?
a. $ 8,246.00 b. $116,937.04 c. $131,390.46 d. $164,592.62 e. $190,297.04
PV of an uneven CF stream Answer: a Diff: M
72. You are given the following cash flows. What is the present value
(t = 0) if the discount rate is 12 percent?
0 1 2 3 4 5 6 Periods | | | | | | | 0 1 2,000 2,000 2,000 0 -2,000 a. $3,277 b. $4,804 c. $5,302 d. $4,289 e. $2,804 12%
PV of uncertain cash flows Answer: e Diff: M
73. A project with a 3-year life has the following probability
distributions for possible end-of-year cash flows in each of the next three years:
Year 1 Year 2 Year 3
Prob Cash Flow Prob Cash Flow Prob Cash Flow 0.30 $300 0.15 $100 0.25 $200 0.40 500 0.35 200 0.75 800 0.30 700 0.35 600
0.15 900
Using an interest rate of 8 percent, find the expected present value of these uncertain cash flows. (Hint: Find the expected cash flow in each year, then evaluate those cash flows.)
a. $1,204.95 b. $ 835.42 c. $1,519.21 d. $1,580.00 e. $1,347.61
Value of missing cash flow Answer: d Diff: M
74. Foster Industries has a project that has the following cash flows:
Year Cash Flow
0 -$300.00
1 100.00
2 125.43
3 90.12
4 ?
What cash flow will the project have to generate in the fourth year in order for the project to have a 15 percent rate of return?
a. $ 15.55 b. $ 58.95 c. $100.25 d. $103.10 e. $150.75
Value of missing cash flow Answer: c Diff: M
75. John Keene recently invested $2,566.70 in a project that is promising
to return 12 percent per year. The cash flows are expected to be as follows:
End of Year Cash Flow
1 $325 2 400 3 550 4 ? 5 750 6 800
What is the cash flow at the end of the 4th year?
a. $1,187 b. $ 600 c. $1,157 d. $ 655 e. $1,267
Value of missing payments Answer: d Diff: M
76. You recently purchased a 20-year investment that pays you $100 at t =
1, $500 at t = 2, $750 at t = 3, and some fixed cash flow, X, at the end of each of the remaining 17 years. You purchased the investment for $5,544.87. Alternative investments of equal risk have a required return of 9 percent. What is the annual cash flow received at the end of each of the final 17 years, that is, what is X?
a. $600 b. $625 c. $650 d. $675 e. $700
Value of missing payments Answer: c Diff: M
77. A 10-year security generates cash flows of $2,000 a year at the end of
each of the next three years (t = 1, 2, and 3). After three years, the security pays some constant cash flow at the end of each of the next six years (t = 4, 5, 6, 7, 8, and 9). Ten years from now (t = 10) the security will mature and pay $10,000. The security sells for $24,307.85 and has a yield to maturity of 7.3 percent. What annual cash flow does the security pay for years 4 through 9?
a. $2,995 b. $3,568
c. $3,700
d. $3,970 e. $4,296
Value of missing payments Answer: d Diff: M
78. An investment costs $3,000 today and provides cash flows at the end of
each year for 20 years. The investment’s expected return is 10 percent. The projected cash flows for Years 1, 2, and 3 are $100, $200, and $300, respectively. What is the annual cash flow received for each of Years 4 through 20 (17 years)? (Assume the same payment for each of these years.) a. $285.41 b. $313.96 c. $379.89 d. $417.87 e. $459.66
Amortization Answer: c Diff: M
79. If you buy a factory for $250,000 and the terms are 20 percent down,
the balance to be paid off over 30 years at a 12 percent rate of interest on the unpaid balance, what are the 30 equal annual payments? a. $20,593
b. $31,036
c. $24,829
d. $50,212 e. $ 6,667
Amortization Answer: a Diff: M
80. You have just taken out an installment loan for $100,000. Assume that
the loan will be repaid in 12 equal monthly installments of $9,456 and that the first payment will be due one month from today. How much of your third monthly payment will go toward the repayment of principal? a. $7,757.16
b. $6,359.12 c. $7,212.50 d. $7,925.88 e. $8,333.33
Amortization Answer: c Diff: M
81. A homeowner just obtained a $90,000 mortgage. The mortgage is for 30
years (360 months) and has a fixed nominal annual rate of 9 percent, with monthly payments. What percentage of the total payments made the first two years will go toward payment of interest?
a. 89.30% b. 91.70% c. 92.59% d. 93.65% e. 94.76%
Amortization Answer: e Diff: M
82. You recently obtained a $135,000, 30-year mortgage with a nominal
interest rate of 7.25 percent. Assume that payments are made at the end of each month. What portion of the total payments made during the fourth year will go towards the repayment of principal?
a. 9.70% b. 15.86% c. 13.75% d. 12.85% e. 14.69%
Amortization Answer: b Diff: M
83. John and Peggy recently bought a house, and they financed it with a
$125,000, 30-year mortgage with a nominal interest rate of 7 percent. Mortgage payments are made at the end of each month. What portion of their mortgage payments during the first three years will go towards repayment of principal? a. 12.81% b. 13.67% c. 14.63% d. 15.83% e. 17.14%
Amortization Answer: b Diff: M N
84. The Taylor family has a $250,000 mortgage. The mortgage is for 15
years, and has a nominal rate of 8 percent. Mortgage payments are due at the end of each month. What percentage of the monthly payments during the fifth year goes towards repayment of principal?
a. 46.60% b. 43.16% c. 57.11% d. 19.32% e. 56.84%
Remaining mortgage balance Answer: b Diff: M N
85. The Bunker Family recently entered into a 30-year mortgage for
$300,000. The mortgage has an 8 percent nominal interest rate. Interest is compounded monthly, and all payments are due at the end of the month. What will be the remaining balance on the mortgage after five years? a. $ 14,790.43 b. $285,209.57 c. $300,000.00 d. $366,177.71 e. $298,980.02
Remaining loan balance Answer: d Diff: M
86. Jamie and Jake each recently bought a different new car. Both received
a loan from a local bank. Both loans have a nominal interest rate of 12 percent with payments made at the end of each month, are fully amortizing, and have the same monthly payment. Jamie’s loan is for $15,000; however, his loan matures at the end of 4 years (48 months), while Jake’s loan matures in 5 years (60 months). After 48 months Jamie’s loan will be paid off. At the end of 48 months what will be the remaining balance on Jake’s loan?
a. $ 1,998.63 b. $ 2,757.58 c. $ 3,138.52 d. $ 4,445.84 e. $11,198.55
Effective annual rate Answer: b Diff: M
87. If it were evaluated with an interest rate of 0 percent, a 10-year
regular annuity would have a present value of $3,755.50. If the future (compounded) value of this annuity, evaluated at Year 10, is $5,440.22, what effective annual interest rate must the analyst be using to find the future value?
a. 7% b. 8% c. 9% d. 10% e. 11%
Effective annual rate Answer: d Diff: M
88. Steaks Galore needs to arrange financing for its expansion program. One
bank offers to lend the required $1,000,000 on a loan that requires interest to be paid at the end of each quarter. The quoted rate is 10 percent, and the principal must be repaid at the end of the year. A second lender offers 9 percent, daily compounding (365-day year), with interest and principal due at the end of the year. What is the difference in the effective annual rates (EFF%) charged by the two banks? a. 0.31%
b. 0.53% c. 0.75% d. 0.96% e. 1.25%
Effective annual rate Answer: e Diff: M
89. You have just taken out a 10-year, $12,000 loan to purchase a new car.
This loan is to be repaid in 120 equal end-of-month installments. If each of the monthly installments is $150, what is the effective annual interest rate on this car loan?
a. 6.5431% b. 7.8942% c. 8.6892% d. 8.8869%
e. 9.0438% +
Nominal vs. effective annual rate Answer: b Diff: M N 90. Gilhart First National Bank offers an investment security with a 7.5
percent nominal annual return, compounded quarterly. Gilhart’s competitor, Olsen Savings and Loan, is offering a similar security that bears the same risk and same effective rate of return. However, Olsen’s security pays interest monthly. What is the nominal annual return of the security offered by Olsen?
a. 7.39% b. 7.45% c. 7.50% d. 7.54% e. 7.59%
Effective annual rate and annuities Answer: d Diff: M
91. You plan to invest $5,000 at the end of each of the next 10 years in an
account that has a 9 percent nominal rate with interest compounded monthly. How much will be in your account at the end of the 10 years? a. $ 75,965
b. $967,571 c. $ 84,616 d. $ 77,359 e. $ 80,631
Value of a perpetuity Answer: c Diff: M
92. You are willing to pay $15,625 to purchase a perpetuity that will pay
you and your heirs $1,250 each year, forever. If your required rate of return does not change, how much would you be willing to pay if this were a 20-year annual payment, ordinary annuity instead of a perpetuity? a. $10,342
b. $11,931
c. $12,273
d. $13,922 e. $17,157
EAR and FV of an annuity Answer: b Diff: M 93. An investment pays you $5,000 at the end of each of the next five
years. Your plan is to invest the money in an account that pays 8 percent interest, compounded monthly. How much will you have in the account after receiving the final $5,000 payment in 5 years (60 months)? a. $ 25,335.56
b. $ 29,508.98 c. $367,384.28 d. $304,969.90 e. $ 25,348.23
Required annuity payments Answer: c Diff: M
94. A baseball player is offered a 5-year contract that pays him the
following amounts: Year 1: $1.2 million Year 2: 1.6 million Year 3: 2.0 million Year 4: 2.4 million Year 5: 2.8 million
Under the terms of the agreement all payments are made at the end of each year.
Instead of accepting the contract, the baseball player asks his agent to negotiate a contract that has a present value of $1 million more than that which has been offered. Moreover, the player wants to receive his payments in the form of a 5-year annuity due. All cash flows are discounted at 10 percent. If the team were to agree to the player’s terms, what would be the player’s annual salary (in millions of dollars)? a. $1.500 b. $1.659 c. $1.989 d. $2.343 e. $2.500
Required annuity payments Answer: b Diff: M
95. Karen and her twin sister, Kathy, are celebrating their 30th birthday
today. Karen has been saving for her retirement ever since their 25th
birthday. On their 25th birthday, she made a $5,000 contribution to her
retirement account. Every year thereafter on their birthday, she has added another $5,000 to the account. Her plan is to continue
contributing $5,000 every year on their birthday. Her 41st, and final,
$5,000 contribution will occur on their 65th birthday.
So far, Kathy has not saved anything for her retirement but she wants to begin today. Kathy’s plan is to also contribute a fixed amount
every year. Her first contribution will occur today, and her 36th, and
final, contribution will occur on their 65th birthday. Assume that both
investment accounts earn an annual return of 10 percent. How large does Kathy’s annual contribution have to be for her to have the same amount in her account at age 65, as Karen will have in her account at age 65? a. $9,000.00 b. $8,154.60 c. $7,398.08 d. $8,567.20 e. $7,933.83
Required annuity payments Answer: c Diff: M
96. Jim and Nancy just got married today. They want to start saving so
they can buy a house five years from today. The average house in their town today sells for $120,000. Housing prices are expected to increase 3 percent a year. When they buy their house five years from now, Jim and Nancy expect to get a 30-year (360-month) mortgage with a 7 percent nominal interest rate. They want the monthly payment on their mortgage to be $500 a month.
Jim and Nancy want to buy an average house in their town. They are starting to save today for a down payment on the house. The down payment plus the mortgage will equal the expected price of the house. Their plan is to deposit $2,000 in a brokerage account today and then deposit a fixed amount at the end of each of the next five years. Assuming that the brokerage account has an annual return of 10 percent, how much do Jim and Nancy need to deposit at the end of each year in order to accomplish their goal?
a. $10,634 b. $ 9,044 c. $ 9,949 d. $ 9,421 e. $34,569
Required annuity payments Answer: a Diff: M N
97. Today is your 25th birthday. Your goal is to have $2 million by the
time you retire at age 65. So far you have nothing saved, but you plan on making the first contribution to your retirement account today. You plan on making three other contributions to the account, one at age 30, age 35, and age 40. Since you expect that your income will increase rapidly over the next several years, the amount that you contribute at age 30 will be double what you contribute today, the amount at age 35 will be three times what you contribute today, and the amount at age 40 will be four times what you contribute today. Assume that your investments will produce an average annual return of 10 percent. Given your goal and plan, what is the minimum amount you need to contribute to your account today?
a. $10,145 b. $10,415 c. $10,700 d. $10,870 e. $11,160
NPV and non-annual discounting Answer: b Diff: M
98. Your lease calls for payments of $500 at the end of each month for the
next 12 months. Now your landlord offers you a new 1-year lease that calls for zero rent for 3 months, then rental payments of $700 at the end of each month for the next 9 months. You keep your money in a bank time deposit that pays a nominal annual rate of 5 percent. By what amount would your net worth change if you accept the new lease? (Hint: Your return per month is 5%/12 = 0.4166667%.)
a. -$509.81 b. -$253.62 c. +$125.30 d. +$253.62 e. +$509.81
Tough:
PV of an uneven CF stream Answer: c Diff: T
99. Find the present value of an income stream that has a negative flow of
$100 per year for 3 years, a positive flow of $200 in the 4th year, and
a positive flow of $300 per year in Years 5 through 8. The appropriate discount rate is 4 percent for each of the first 3 years and 5 percent for each of the later years. Thus, a cash flow accruing in Year 8 should be discounted at 5 percent for some years and 4 percent in other years. All payments occur at year-end.
a. $ 528.21 b. $1,329.00 c. $ 792.49 d. $1,046.41
PV of an uneven CF stream Answer: d Diff: T 100. Hillary is trying to determine the cost of health care to college
students and parents’ ability to cover those costs. She assumes that the cost of one year of health care for a college student is $1,000 today, that the average student is 18 when he or she enters college, that inflation in health care cost is rising at the rate of 10 percent per year, and that parents can save $100 per year to help cover their children’s costs. All payments occur at the end of the relevant period, and the $100/year savings will stop the day the child enters college (hence 18 payments will be made). Savings can be invested at a nominal rate of 6 percent, annual compounding. Hillary wants a health care plan that covers the fully inflated cost of health care for a student for 4 years, during Years 19 through 22 (with payments made at the end of Years 19 through 22). How much would the government have to set aside now (when a child is born), to supplement the average parent’s share of a child’s college health care cost? The lump sum the government sets aside will also be invested at 6 percent, annual compounding. a. $1,082.76 b. $3,997.81 c. $5,674.23 d. $7,472.08 e. $8,554.84
Required annuity payments Answer: b Diff: T
101. You are saving for the college education of your two children. One
child will enter college in 5 years, while the other child will enter college in 7 years. College costs are currently $10,000 per year and are expected to grow at a rate of 5 percent per year. All college costs are paid at the beginning of the year. You assume that each child will be in college for four years.
You currently have $50,000 in your educational fund. Your plan is to contribute a fixed amount to the fund over each of the next 5 years. Your first contribution will come at the end of this year, and your final contribution will come at the date when you make the first tuition payment for your oldest child. You expect to invest your contributions into various investments, which are expected to earn 8 percent per year. How much should you contribute each year in order to meet the expected cost of your children’s education?
a. $2,894 b. $3,712 c. $4,125 d. $5,343 e. $6,750
Required annuity payments Answer: b Diff: T
102. A young couple is planning for the education of their two children.
They plan to invest the same amount of money at the end of each of the next 16 years. The first contribution will be made at the end of the year and the final contribution will be made at the end of the year the older child enters college.
The money will be invested in securities that are certain to earn a return of 8 percent each year. The older child will begin college in 16 years and the second child will begin college in 18 years. The parents anticipate college costs of $25,000 a year (per child). These costs must be paid at the end of each year. If each child takes four years to complete their college degrees, then how much money must the couple save each year?
a. $ 9,612.10 b. $ 5,477.36 c. $12,507.29 d. $ 5,329.45 e. $ 4,944.84
Required annuity payments Answer: c Diff: T
103. Your father, who is 60, plans to retire in 2 years, and he expects to live
independently for 3 years. He wants a retirement income that has, in the first year, the same purchasing power as $40,000 has today. However, his retirement income will be a fixed amount, so his real income will decline over time. His retirement income will start the day he retires, 2 years from today, and he will receive a total of 3 retirement payments.
Inflation is expected to be constant at 5 percent. Your father has $100,000 in savings now, and he can earn 8 percent on savings now and in the future. How much must he save each year, starting today, to meet his retirement goals?
a. $1,863 b. $2,034 c. $2,716 d. $5,350 e. $6,102
Required annuity payments Answer: d Diff: T
104. Your father, who is 60, plans to retire in 2 years, and he expects to
live independently for 3 years. Suppose your father wants to have a real income of $40,000 in today’s dollars in each year after he retires. His retirement income will start the day he retires, 2 years from today, and he will receive a total of 3 retirement payments.
Inflation is expected to be constant at 5 percent. Your father has $100,000 in savings now, and he can earn 8 percent on savings now and in the future. How much must he save each year, starting today, to meet his retirement goals?
a. $1,863 b. $2,034 c. $2,716 d. $5,350 e. $6,102
Required annuity payments Answer: c Diff: T
105. You are considering an investment in a 40-year security. The security
will pay $25 a year at the end of each of the first three years. The security will then pay $30 a year at the end of each of the next 20 years. The nominal interest rate is assumed to be 8 percent, and the current price (present value) of the security is $360.39. Given this information, what is the equal annual payment to be received from Year 24 through Year 40 (for 17 years)?
a. $35 b. $38 c. $40 d. $45 e. $50
Required annuity payments Answer: a Diff: T
106. John and Jessica are saving for their child’s education. Their
daughter is currently eight years old and will be entering college 10 years from now (t = 10). College costs are currently $15,000 a year and are expected to increase at a rate of 5 percent a year. They expect their daughter to graduate in four years, and that all annual payments will be due at the beginning of each year (t = 10, 11, 12, and 13).
Right now, John and Jessica have $5,000 in their college savings account. Starting today, they plan to contribute $3,000 a year at the beginning of each of the next five years (t = 0, 1, 2, 3, and 4). Then their plan is to make six equal annual contributions at the end of each of the following six years (t = 5, 6, 7, 8, 9, and 10). Their investment account is expected to have an annual return of 12 percent. How large of an annual payment do they have to make in the subsequent six years (t = 5, 6, 7, 8, 9, and 10) in order to meet their child’s anticipated college costs?
a. $4,411 b. $7,643 c. $2,925 d. $8,015 e. $6,798
Required annuity payments Answer: a Diff: T
107. Today is Rachel’s 30th birthday. Five years ago, Rachel opened a
brokerage account when her grandmother gave her $25,000 for her 25th
birthday. Rachel added $2,000 to this account on her 26th birthday,
$3,000 on her 27th birthday, $4,000 on her 28th birthday, and $5,000 on
her 29th birthday. Rachel’s goal is to have $400,000 in the account by
her 40th birthday.
Starting today, she plans to contribute a fixed amount to the account each year on her birthday. She will make 11 contributions, the first
one will occur today, and the final contribution will occur on her 40th
birthday. Complicating things somewhat is the fact that Rachel plans
to withdraw $20,000 from the account on her 35th birthday to finance the
down payment on a home. How large does each of these 11 contributions have to be for Rachel to reach her goal? Assume that the account has earned (and will continue to earn) an effective return of 12 percent a year. a. $11,743.95 b. $10,037.46 c. $11,950.22 d. $14,783.64 e. $ 9,485.67
Required annuity payments Answer: c Diff: T
108. John is saving for his retirement. Today is his 40th birthday. John
first started saving when he was 25 years old. On his 25th birthday,
John made the first contribution to his retirement account; he deposited $2,000 into an account that paid 9 percent interest, compounded monthly. Each year on his birthday, John contributes another
$2,000 to the account. The 15th (and last) contribution was made last
year on his 39th birthday.
John wants to close the account today and move the money to a stock fund that is expected to earn an effective return of 12 percent a year. John’s plan is to continue making contributions to this new account each year on his birthday. His next contribution will come today (age
40) and his final planned contribution will be on his 65th birthday. If
John wants to accumulate $3,000,000 in his account by age 65, how much must he contribute each year until age 65 (26 contributions in all) to achieve his goal?
a. $11,892 b. $13,214 c. $12,471 d. $10,388 e. $15,572
Required annuity payments Answer: a Diff: T
109. Joe and Jane are interested in saving money to put their two children,
John and Susy through college. John is currently 12 years old and will enter college in six years. Susy is 10 years old and will enter college in 8 years. Both children plan to finish college in four years. College costs are currently $15,000 a year (per child), and are expected to increase at 5 percent a year for the foreseeable future. All college costs are paid at the beginning of the school year. Up until now, Joe and Jane have saved nothing but they expect to receive $25,000 from a favorite uncle in three years.
To provide for the additional funds that are needed, they expect to make 12 equal payments at the beginning of each of the next 12 years--the first payment will be made today and years--the final payment will be made on Susy’s 21st birthday (which is also the day that the last payment
must be made to the college). If all funds are invested in a stock fund that is expected to earn 12 percent, how large should each of the annual contributions be?
a. $ 7,475.60 b. $ 7,798.76 c. $ 8,372.67 d. $ 9,675.98 e. $14,731.90
Required annuity payments Answer: b Diff: T 110. John and Barbara Roberts are starting to save for their daughter’s
college education.
• Assume that today’s date is September 1, 2002.
• College costs are currently $10,000 a year and are expected to
increase at a rate equal to 6 percent per year for the foreseeable future. All college payments are due at the beginning of the year. (So for example, college will cost $10,600 for the year beginning September 1, 2003).
• Their daughter will enter college 15 years from now (September 1, 2017). She will be enrolled for four years. Therefore the Roberts will need to make four tuition payments. The first payment will be made on September 1, 2017, the final payment will be made on September 1, 2020. Notice that because of rising tuition costs, the tuition payments will increase each year.
• The Roberts would also like to give their daughter a lump-sum
payment of $50,000 on September 1, 2021, in order to help with a down payment on a home, or to assist with graduate school tuition.
• The Roberts currently have $10,000 in their college account. They
anticipate making 15 equal contributions to the account at the end of each of the next 15 years. (The first contribution would be made on September 1, 2003, the final contribution will be made on September 1, 2017).
• All current and future investments are assumed to earn an 8 percent
return. (Ignore taxes.)
How much should the Roberts contribute each year in order to reach their goal? a. $3,156.69 b. $3,618.95 c. $4,554.83 d. $5,955.54 e. $6,279.54
Required annuity payments Answer: a Diff: T
111. Joe and June Green are planning for their children’s college education.
Joe would like his kids to attend his alma mater where tuition is currently $25,000 per year. Tuition costs are expected to increase by 5 percent each year. Their children, David and Daniel, just turned 2 and 3 years old today, September 1, 2002. They are expected to begin college the year in which they turn 18 years old and each will complete his schooling in four years. College tuition must be paid at the beginning of each school year.
Grandma Green invested $10,000 in a mutual fund the day each child was born. This was to begin the boys’ college fund (a combined fund for both children). The investment has earned and is expected to continue to earn 12 percent per year. Joe and June will now begin adding to
this fund every August 31st (beginning with August 31, 2003) to ensure
that there is enough money to send the kids to college.
How much money must Joe and June put into the college fund each of the next 15 years if their goal is to have all of the money in the investment account by the time Daniel (the oldest son) begins college? a. $5,928.67
b. $7,248.60 c. $4,822.66 d. $7,114.88 e. $5,538.86
Required annuity payments Answer: a Diff: T
112. Jerry and Donald are two brothers with the same birthday. Today is
Jerry’s 30th birthday and Donald’s 25th birthday. Donald has been saving
for retirement ever since his 20th birthday, when he started his
retirement account with a $10,000 contribution. Every year since, Donald has contributed $5,000 to the account on his birthday. He plans
to make the 40th, and final, $5,000 contribution on his 60th birthday,
after which he plans to retire. In other words, by the time Donald has made all of his contributions he will have made one contribution of $10,000 followed by 40 annual contributions of $5,000.
Jerry plans to retire on the same day (which will be his 65th birthday);
however, until now, he has saved nothing for retirement. Jerry’s plan is to start contributing a fixed amount each year on his birthday; the first
contribution will occur today. Jerry’s 36th, and final, contribution will
occur on his 65th birthday. Jerry’s goal is to have the same amount when
he retires at age 65 that Donald will have at age 60. Assume that both accounts have an expected annual return of 12 percent. How much does Jerry need to contribute each year in order to meet his goal?
a. $ 9,838 b. $ 9,858 c. $ 9,632 d. $10,788 e. $11,041
